Details

sample56.0ms

Algorithm

intervals

Results

14.0ms	124×	body	160	valid
13.0ms	236×	body	80	nan
8.0ms	132×	body	80	valid

simplify128.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	10
1	51	10
2	107	10
3	290	10
4	1054	10
5	4445	10
6	5001	10

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.2b	(pow (/ Om Omc) 2.0)
0.7b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
10.5b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
46×	`times-frac`
38×	`*-un-lft-identity`
32×	`add-cube-cbrt` `unpow-prod-down`
30×	`sqrt-prod`
12×	`difference-of-squares`
10×	`add-exp-log`
7×	`pow1`
6×	`pow-unpow`
5×	`sqr-pow`
4×	`expm1-log1p-u` `pow-exp` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`div-inv` `distribute-lft-out--`
2×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `div-exp` `associate-/r/`
1×	`asin-acos` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+`

Counts

4 → 114

Calls

4 calls:

5.0ms	(pow (/ t l) 2.0)
5.0ms	(pow (/ Om Omc) 2.0)
1.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
13.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series484.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(pow (/ t l) 2.0)
66.0ms	(pow (/ Om Omc) 2.0)
18.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
333.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify57.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	709	1289
1	2087	1218
2	5001	1206

prune528.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 11.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.4b	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.7b	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
10.3b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

108×	`add-sqr-sqrt`
95×	`sqrt-prod`
82×	`times-frac`
65×	`*-un-lft-identity`
51×	`add-cube-cbrt`
28×	`difference-of-squares`
27×	`unpow-prod-down`
11×	`associate-/l*`
9×	`add-exp-log`
8×	`sqr-pow`
7×	`distribute-lft-out--`
6×	`pow1` `sqrt-div` `associate-/r*` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`flip3-+` `div-exp` `pow-exp` `associate-/r/` `flip-+` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `asin-acos` `sqrt-undiv` `flip3--` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `flip--`

Counts

4 → 159

Calls

4 calls:

5.0ms	(pow (/ Om Omc) 2.0)
19.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
1.0ms	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
3.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series734.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(pow (/ Om Omc) 2.0)
327.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
18.0ms	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
326.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify64.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	624	2554
1	2015	2381
2	5002	2370

prune629.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 11.3b

localize25.0ms

Local error

Found 4 expressions with local error:

10.3b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
12.9b	(cbrt (/ Om Omc))
12.9b	(cbrt (/ Om Omc))
12.9b	(cbrt (/ Om Omc))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

39×	`cbrt-prod`
27×	`add-sqr-sqrt` `times-frac`
26×	`add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div` `pow1/3` `sqrt-prod` `div-inv`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 89

Calls

4 calls:

3.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms	(cbrt (/ Om Omc))
3.0ms	(cbrt (/ Om Omc))
3.0ms	(cbrt (/ Om Omc))

series372.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
63.0ms	(cbrt (/ Om Omc))
65.0ms	(cbrt (/ Om Omc))
62.0ms	(cbrt (/ Om Omc))

simplify81.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	257	606
1	712	580
2	2865	573
3	5002	549

prune537.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.2b	(pow (/ Om Omc) 2.0)
0.7b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
10.5b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
46×	`times-frac`
38×	`*-un-lft-identity`
32×	`add-cube-cbrt` `unpow-prod-down`
30×	`sqrt-prod`
12×	`difference-of-squares`
10×	`add-exp-log`
7×	`pow1`
6×	`pow-unpow`
5×	`sqr-pow`
4×	`expm1-log1p-u` `pow-exp` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`div-inv` `distribute-lft-out--`
2×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `div-exp` `associate-/r/`
1×	`asin-acos` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+`

Counts

4 → 114

Calls

4 calls:

5.0ms	(pow (/ t l) 2.0)
5.0ms	(pow (/ Om Omc) 2.0)
1.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
16.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series474.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(pow (/ t l) 2.0)
63.0ms	(pow (/ Om Omc) 2.0)
18.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
328.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify60.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	709	1289
1	2087	1218
2	5001	1206

prune547.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 11.3b

regimes783.0ms

Accuracy

0% (0.1b remaining)

Error of 10.7b against oracle of 10.6b and baseline of 10.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	19
1	24	19

end0.0ms

sample1.6s

Algorithm

intervals

Results

458.0ms	7956×	body	80	nan
455.0ms	3753×	body	160	valid
244.0ms	4247×	body	80	valid